Mathematical Model Helps Design Efficient Multi-Drug Therapies

New research conducted by Harvard scientists could help explain why adherence to a drug regimen and resistance is different for each of the drugs that make up the "cocktail" used to treat HIV and may help doctors quickly and cheaply design new combinations of drugs.

A paper published in the September 2 issue of Nature Medicine describes how a team of researchers led by Martin Nowak, Harvard Professor of Mathematics and of Biology and Director of the Program for Evolutionary Dynamics, have developed a technique medical researchers can use to model the effects of various treatments, and predict whether they will cause the virus to develop resistance.

"What we demonstrate in this paper is a prototype for predicting, through modeling, whether a patient at a given adherence level is likely to develop resistance to treatment," said Alison Hill, a PhD student in Biophysics and one of the lead authors of the paper. "Compared to the time and expense of a clinical trial, this method offers a relatively easy way to make these predictions. And, as we show in the paper, our results match with what doctors are seeing in clinical settings."

The hope, said Nowak, is that the new technique will take some of the guesswork out of what is now largely a trial-and-error process. "This is a mathematical tool that will help design clinical trials," he said. "Right now, researchers are using trial and error to develop these combination therapies. Our approach uses the mathematical understanding of evolution to make the process more akin to engineering."

Creating a model that can make such predictions accurately, however, requires huge amounts of data. To get that data, Hill and Daniel Scholes Rosenbloom, a PhD student in Organismic and Evolutionary Biology and the paper's other lead author, turned to Johns Hopkins University Medical School, where Robert F. Siliciano, Professor of Medicine and of Molecular Biology and Genetics, was working with PhD student Alireza Rabi to study how HIV reacted to varying drug dosages.

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Such data proved critical to the model that Hill, Rabi, and Rosenbloom eventually designed, because the level of the drug in patients -- even those that adhere to their treatment perfectly -- naturally varies. When drug levels are low, as they are between doses or if a dose is missed, the virus is better able to replicate and grow. Higher drug levels may keep the virus in check, but they also increase the risk of mutant strains of the virus emerging, leading to drug resistance.

Armed with the data from Johns Hopkins, Hill, Rabi, and Rosenbloom created a computer model that could predict whether and how much the virus, or a drug-resistant strain, was growing based on how strictly patients stuck to their drug regimen.

"Our model is essentially a simulation of what goes on during treatment," Rosenbloom explained. "We created a number of simulated patients, each of whom had different characteristics, and then we said, 'Let's imagine these patients have 60% adherence to their treatment -- they take 60% of the pills they're supposed to.' Our model can tell us what their drug concentration is over time, and based on that, we can say whether the virus is growing or shrinking, and whether they're likely to develop resistance." The model's predictions can then serve as a guide to researchers as they work to design new drug cocktails to combat HIV.

While their model does hold out hope for simplifying the process of designing drug "cocktails," Hill and Rosenbloom said they plan to continue to refine the model to take additional factors into effect, such as multiple mutant-resistant strains of the virus and varying drug concentrations in other parts of the body.

Ultimately, though, both say their model can offer new hope to patients by helping doctors design better, cheaper, and more efficient treatments.

"Over the past 10 years, the number of HIV-infected people receiving drug treatment has increased immensely," Hill said. "Figuring out what the best ways are to treat people in terms of cost effectiveness, adherence, and the chance of developing resistance is going to become even more important."

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